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Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$
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$\int_{1}^{e}4x\ln\left(x\right)dx$
Learn how to solve equations problems step by step online. Integrate the function xln(x^4) from 1 to e. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). The integral of a constant times a function is equal to the constant multiplied by the integral of the function. We can solve the integral \int x\ln\left(x\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du.